Question 1

Given the relation $$\{(0,3), (5,2), (4,-3)\}$$, which statement best describes whether this relation represents a function?

Accepted Answer

Yes, because for each element in the domain, there is exactly one corresponding element in the range.

Question 2

Evaluate the function $$f(y) = 3 - 4y at$$ $$y = -5. $$What is $$f(-5)$$?

Accepted Answer

$$23$$

Question 3

Which of the following functions is classified as a root function, and what is its domain?

Accepted Answer

$$f(t) = 5 - 7t - 4$$; domain: $$(-\infty, \infty)$$

Question 4

For the function $$g(x) = 15$$, what are the $$x-$$intercept(s) and $$y-$$intercept?

Accepted Answer

There is no $$x-$$intercept; the $$y-$$intercept is $$y = 15$$

Question 5

Given the graph of a function with domain $$[-2, 3]$$ and range $$[6, 8]$$, which of the following is correct?

Accepted Answer

Domain: $$[-2, 3]$$, Range: $$[6, 8]$$

Question 6

A function is increasing on the intervals $$(-\infty, -6)$$ and $$(-1, 0)$$, decreasing on $$(-6, -4)$$, and constant on $$(-4, -1)$$ and $$(0, \infty). $$Which statement is true?

Accepted Answer

The function is increasing on $$(-\infty, -6)$$ and $$(-1, 0).$$

Question 7

Given a function with a relative minimum at $$x = -11$$ with value $$-121$$, and a relative maximum at $$x = 11$$ with value $$121$$, which of the following is correct?

Accepted Answer

Relative minimum at $$x = -11 is$$ $$-121$$, relative maximum at $$x = 11 is$$ $$121$$

Question 8

Determine whether the function $$f(x) = x^4$ - 2x^2$ + 7 is $$even, odd, or neither.

Accepted Answer

The function is even.

Question 9

Which of the following properties apply to the function $$f(x) = x$$?

Accepted Answer

The function is odd, linear, domain $$(-\infty, \infty)$$, range $$(-\infty, \infty)$$, and increasing on $$(-\infty, \infty).$$

Question 10

Sketch the graph of $$f(x) = \frac{1}{x}$$ for $$-2 \u003c x \leq 2. $$What is the domain in interval notation?

Accepted Answer

$$(-2, 2]$$

Question 11

Given the function $$f(x) = x^3$ with domain x$$ \geq -4$$, how would you express the domain and the function using an inequality?

Accepted Answer

Domain: $$[-4, \infty)$$; Function: $$f(x) = x^3$ for x$$ \geq -4$$

Question 12

If the graph of $$y = x is $$shifted horizontally to the right by 3 units, what is the new function?

Accepted Answer

$$f(x) = x - 3$$

Question 13

Given the function $$f(x)$$ and its graph, if $$y = -f(x)$$, which transformation occurs?

Accepted Answer

The graph is reflected over the $$x-$$axis.

Question 14

Given $$f(x) = x + 9$$ and $$g(x) = x^2$ - 3$$, what is $$\frac{f(0)}{g(0)}$$?

Accepted Answer

$$1/2$$

Question 15

For the pair of functions $$f(x) = x^2$ - 1$$ and $$g(x) = 5x + 15$$, what is $$(f + g)(x)$$?

Accepted Answer

$$x^2 + 5x + 14$

Question 16

Given $$f(x) = -7$$ and $$g(x) = x + 31$$, what is $$(g \circ f)(1)$$?

Accepted Answer

$$24$$

Question 17

Given $$g(x) = 8$$ and $$h(x) = x + 12$$, what is $$(g + h)(x)$$?

Accepted Answer

$$x + 20$$

Question 18

Is the function $$f(x) = 2^3$ one-to-one?

Accepted Answer

No

Question 19

Given $$f(x) = 13 - x$$ and $$g(x) = \frac{13}{x + 1}$$, are $$f$$ and $$g$$ inverse functions of each other?

Accepted Answer

Yes, because $$f(g(x)) = x$$ and $$g(f(x)) = x$$

College Algebra Chapter 3 Practice Test – Step-by-Step Study Guidance

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